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Labeling the gases in a system as "ideal" means that the molecules occupy no space and that intermolecular attractions are negligible. We use the concepts of ideal gas laws to approximate the best-case scenario in a system. An ideal system does not have to be under conditions fo constant volume or pressure. However, we can use this information and the ideal gas law, PV = nRT, to solve problems involving ideal gases.
I believe the term "ideal" is used to describe gases, not systems. Ideal gases are those in which the forces of attraction between the molecules are negligible, and the molecules occupy a very small fraction of the space (taken to be as zero). You must know a gas is ideal before getting involved with any calculations related to the equation PV = nRT.
The point of telling us that a gas is ideal and monoatomic is so that we know we can use the constants Cv= 3/2R and Cp= 5/2R.This allows us to calculate work and entropy when only either volume or pressure remains constant, or the reaction is reversible.
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